Randomly inverting pulse polarity in an UWB signal for power spectrum density shaping

ABSTRACT

A method eliminates spectral lines in a time hopping ultra wide bandwidth signal. First, a train of pulses is generated from input symbols. The pulses are then modulated in time according to symbols. The modulation can use pulse position modulation and time hopping. A polarity of the pulses is inverted randomly before transmitting the pulses as an ultra wide bandwidth signal. By randomly inverting the polarity of the pulses spectral lines in the ultra wide bandwidth signal are eliminated.

FIELD OF THE INVENTION

This invention relates generally to wireless communication, and moreparticularly to communicating with ultra wide bandwidth (UWB) systems.

BACKGROUND OF THE INVENTION

Ultra wide bandwidth (UWB) systems have recently received considerableattention for wireless radio communication systems. Recently, the USFederal Communications Commission (FCC) has allowed UWB systems forlimited indoor and outdoor applications.

The IEEE 802.15.3a standards group has defined performance requirementsfor the use of UWB in short range indoor communication system.Throughput of at least 110 Mbps at 10 meters are required. This meansthat the transmission data rate must be greater. Furthermore, a bit rateof at least 200 Mbps is required at four meters. Scalability to rates inexcess of 480 Mbps is desirable, even when the rates can only beachieved at smaller ranges. These requirements provide a range of valuesfor a pulse repetition frequency (PRF).

In February 2002, the FCC released the “First Order and Report”providing power limits for UWB signals. The average limits over alluseable frequencies are different for indoor and outdoor systems. Theselimits are given in the form of a power spectral density (PSD) mask 200,see FIG. 2. In the frequency band from 3.1 GHz to 10.6 GHz, the PSD islimited to −41.25 dBm/MHz. The limits on the PSD must be fulfilled foreach possible 1 MHz band, but not necessarily for smaller bandwidths

For systems operating above 960 MHz, there is a limit on the peakemission level contained within a 50 MHz bandwidth centered on thefrequency, f_(M), at which the highest radiated emission occurs. The FCChas adopted a peak limit based on a sliding scale dependent on an actualresolution bandwidth (RBW) employed in the measurement. The peak EIRPlimit is 20 log (RBW/50) dBm, when measured with a resolution bandwidthranging from 1 MHz to 50 MHz. Only one peak measurement, centered onf_(M), is required. As a result, UWB emissions are average-limited forPRFs greater than 1 MHz and peak-limited for PRFs below 1 MHz.

These data rate requirements and emission limits result in constraintson the pulse shape, the level of the total power used, the PRF, and thepositions and amplitudes of the spectral lines.

In UWB systems, a train of electromagnetic pulses are used to carrydata. FIG. 1 shows an example symbol structure 100 of UWB signal with aone pulse per frame 101, i.e., the symbol length, a time hopping (TH)sequence of eight pulses 102 or subframes, and a subframe 103 includinga TH margin. The signal comprises symbols 110 equal to a frame length,subframes 111, with a pulse position modulation (PPM) margin 112, and aTH margin 113. Instead of grouping N pulses to create a symbol of Nframe durations, the frame duration is split into N subframes with 1pulse per subframe, as shown in FIG. 1.

Many UWB signals use pulse position modulation (PPM) for modulation, andtime hopping (TH) spreading for multiple access. This results in adithered pulse train. The spectrum of the signal can be obtained byconsidering this dithered signal as a M-PPM signal.

If the modulating sequence is composed of independent and equiprobablesymbols, then the PSD for non-linear memoryless modulation is given byEquation 1 as:

$\begin{matrix}\begin{matrix}{{G_{s}(f)} = {{\frac{1}{M^{2}T_{s}^{2}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}\;\left( {{{\sum\limits_{i = 0}^{M - 1}\;{S_{i}\left( \frac{n}{T_{s}} \right)}}}^{2}{\delta\left( {f - \frac{n}{T_{s}}} \right)}} \right)}} +}} \\{{\frac{1}{T_{s}}\left( {{\sum\limits_{i = 0}^{M - 1}\;{\frac{1}{M} \cdot {{S_{i}(f)}}^{2}}} - {{\sum\limits_{i = 0}^{M - 1}\;{\frac{1}{M} \cdot {S_{i}(f)}}}}^{2}} \right)},}\end{matrix} & (1)\end{matrix}$where M denotes the number of symbols, T_(s) the symbol period or frame,and S_(i) the PSD of the i^(th) symbol of the constellation.

Inherent in PPM, and as shown in FIG. 2, the first term of Equation (1)causes spectral lines which are outside the FCC mask 200. The spectrumof a signal with a 2-PPM usually contains spectral lines spaced by thePRF. Consequently, the amplitude of these spectral lines can be10*log₁₀(T_(s) ⁻¹) dB above the level of the continuous part of thespectrum. That corresponds to 80 dB for the 100 Mbps data rate mandatedby IEEE 802.15a.

The FCC measurement procedures average the power of these spectral linesover the resolution bandwidth. Even then, the power level remains higherthan the threshold, and thus violate the FCC limits or require areduction of the total power. Time hopping is generally used to reducethe problem of spectral lines by reducing their number in a givenfrequency band. However TH does not necessarily attenuate the amplitudeof the remaining spectral lines.

In a non-periodic time hopped pulse train, each individual pulse can bein one of M equally probable positions within its frame. This signal hasthe same spectrum as a M-PPM signal with the same PRF, f_(PR), anduncorrelated modulated data. Increase M enlarges the constellation ofthe PPM, and therefore the number of pulse positions within the frame.If these positions are uniformly spaced within the frame, then all thespectral lines that are not a multiple of M·f_(PR) disappear.

Instead of grouping N pulses to create a symbol of N frame durations,the former frame duration is split into N subframes with one pulse persubframe 102 as shown in FIG. 1. As a consequence, the PRF is N.f_(PR).Hence, this non-periodic TH pulse train is composed of N pulses perframe, and each pulse can take M positions within the duration of asubframe. The spectrum of this pulse train is the same as for a M-PPMsignal with a PRF=N*f_(PR). As a result, the spectral lines are spacedby M.N.f_(PR) when the M pulse positions are uniformly spaced. If M goesto infinity, which is equivalent to a uniform distribution of the pulse,then all spectral lines occur at infinite spacing and thus effectivelyvanish.

However, in order to consider realistic pulse trains that can be used inthe generation of UWB signals, some modifications need to be made. Ifpulses are truly uniformly distributed within each frame, overlaps mayhappen at the junction between subframes when M increases. Margins orguard intervals eliminate these overlaps.

In order to modulate the symbols by PPM, additional margins areintroduced between frames. However, by introducing margins, the uniformdistribution of pulse positions within each subframe is destroyed, whichhas an impact on the spectral lines. Furthermore TH sequence is limitedin time and contributes to the periodicity of the signal and undesirablespectral lines as shown in FIG. 2.

Therefore, there is a need to provide a system and method that caneliminate these undesirable spectral lines.

SUMMARY OF THE INVENTION

Commonly, ultra wide bandwidth (UWB) systems communicate with trains ofshort-duration pulses that have a low duty-cycle. Thus, the energy ofthe radio signal is spread very thinly over a wide range of frequencies.Almost all of the known systems use a combination of time-hopping (TH)spreading for multiple access, and pulse position modulation (PPM) as amodulation format. This combination results in spectral lines thateither lead to a violation of FCC requirements, or require a significantreduction in power, which decreases performance and range of the signal.

The invention provides a method for eliminating spectral lines caused bytransmitting data using PPM and TH sequences. The spectral lines areeliminated by randomly changing the polarity of the pulses of thesignal. Hereinafter, the word ‘random’ means pseudo-random as commonlyused in the art.

Changing the pulse polarity does not have a negative impact on theperformance of the transceiver because the polarity of the signal is notused to carry information. By changing randomly polarity of the pulsesof the signal, the discrete frequency components of the spectrum vanish.Furthermore, this randomization of the polarity can be used to shape thespectrum of the signal.

A method eliminates spectral lines in a time hopping ultra widebandwidth signal. First, a train of pulses is generated. The pulses arethen modulated in time according to symbols. A polarity of the pulses isinverted randomly before transmitting the pulses as an ultra widebandwidth signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a timing diagram of a pulse train signal to be modifiedaccording to the invention;

FIG. 2 is a power spectral density (PSD) graph of a prior art UWBsignal;

FIG. 3 is a timing diagram of a pulse train before modification;

FIG. 4 is a timing diagram of a pulse train after modification accordingto the invention;

FIG. 5 is a pulse train with one pulse per symbol;

FIG. 6 is a prior art PSD of signal of FIG. 5 without modification;

FIG. 7 is pulse train of FIG. 5 with randomly inverted polarity ofpulses;

FIG. 8 is a PSD of the signal of FIG. 7 according to the invention;

FIG. 9 is a block diagram of a system for randomly inverted pulsesaccording to the invention;

FIG. 10 is a pulse train generated by pulse amplitude modulation beforemodification;

FIG. 11 is a PSD of the signal of FIG. 10;

FIG. 12 is a pulse train generated by pulse amplitude modulation aftermodification;

FIG. 13 a PSD of the signal of FIG. 12;

FIG. 14 is a block diagram of a system for generating the signal of FIG.12;

FIG. 15 are pulse trains before and after modification of pulses withinsymbol durations according to the invention;

FIG. 16 are pulse trains before and after modification from symbol tosymbol according to the invention;

FIG. 17 are pulse trains before and after modification within symbolduration according to the invention;

FIG. 18 are pulse trains before and after modification within symbolduration;

FIG. 19 are pulse trains before and after modification from symbol tosymbol;

FIG. 20 are pulse trains before and after modification within symbolduration;

FIG. 21 are pulse trains before and after modification within symbolduration;

FIG. 22 are pulse trains before and after modification from symbol tosymbol;

FIG. 23 are pulse trains before and after modification within symbolduration;

FIG. 24 are pulse trains before and after modification within symbolduration and from symbol to symbol;

FIG. 25 is a PSD of the signal of FIG. 24 after modification;

FIG. 26 is a subwaveform with two pulses of opposite polarity;

FIG. 27 is a time hopping sequence with four subwaveforms; and

FIG. 28 is the PSD of the signal of FIG. 27.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

To solve the problem of discrete frequency components in a spectrum ofan ultra wide bandwidth (UWB) radio signal, the invention invertsrandomly the polarity of pulses. The resultant signal with randomlyinverted polarity pulse is compliant with FCC regulations.

One could use binary phase-shift keying (BPSK) to randomize the polarityof the pulses. BPSK would also reduce the complexity of the system.However, with BPSK, the channel conditions can modify the polarity ofthe signal and destroy the data.

Therefore, the invention inverts the polarity of the pulses to shape thespectrum of the signal without carrying information. Thus, it isunnecessary to have zero mean information symbols to control thespectral characteristics of the modulated signal. The inversions ofpolarity can be applied to symbols, i.e., the set of pulses composing asymbol taken together, as well to individual pulses. The effect of thismodification according to the invention is to eliminate spectral linescaused by, for example, pulse position modulation (PPM), and otherdithering techniques, such as time hopping (TH) spreading used in UWBsystems.

Thus, the method according to the invention solves the problem ofspectral lines caused by non-equiprobable symbols and non-antipodalmodulation schemes at the same time. Furthermore, the polarity of thesignal can be specifically used to shape the spectrum of the UWB signal.

Random Polarity Inversion

FIG. 3 shows a signal 301 that includes a train of pulses to beprocessed according to the invention. The spectrum of the transmittedsignal 301, after pulse position modulation (PPM) and time hopping (TH)spreading, for the purpose of ultra wide bandwidth wirelesscommunication, contains undesirable spectral lines, as shown in FIG. 2.

FIG. 4 shows a transmitted waveform 401 where the polarity of pulses israndomly inverted according to the invention to eliminate the spectrallines.

The discrete part of the spectral density of a pulse train is given byEquation (2) as:

$\begin{matrix}{{{G_{s}(f)} = {\frac{1}{T_{s}^{2}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}\;\left( {{{\sum\limits_{i = 0}^{M - 1}\;{P_{i} \cdot {S_{i}\left( \frac{n}{T_{s}} \right)}}}}^{2}{\delta\left( {f - \frac{n}{T_{s}}} \right)}} \right)}}},} & (2)\end{matrix}$

where, M is the number of symbols, Ts the symbol period, S_(i) is thepower spectral density (PSD) of the i^(th) symbol for Iε[0,M−1], andP_(i) is the probability of the i^(th) symbol.

By changing randomly the polarity of M symbols S_(i), Equation (1) canbe rewritten as a discrete part of the spectral density of a pulse traincomposed of 2*M antipodal symbols.

The symbols of each antipodal pair have the probability P_(i)/2, and theFourier transform S_(i) and −S_(i). As a result, the spectral linesvanish as given by Equation (3):

$\begin{matrix}{{G_{s}(f)} = {{\frac{1}{T_{s}^{2}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}\;\left( {{{\sum\limits_{i = 0}^{M - 1}\;\left( {{\frac{P_{i}}{2} \cdot {S_{i}\left( \frac{n}{T_{s}} \right)}} - {\frac{P_{i}}{2} \cdot {S_{i}\left( \frac{n}{T_{s}} \right)}}} \right)}}^{2}{\delta\left( {f - \frac{n}{T_{s}}} \right)}} \right)}} = 0.}} & (3)\end{matrix}$

There are several polarity inversion embodiments possible consideringthe main idea behind the invention, including:

One pulse per symbol

-   -   Pulse Position Modulation    -   Pulse Amplitude Modulation

Multiple pulses per symbol

-   -   Pulse Position Modulation    -   Random polarity of pulses within the symbol duration    -   Random polarity from symbol to symbol    -   Identical set of different polarities for pulses in the symbol    -   duration

Pulse Amplitude Modulation

-   -   Random polarity of pulses within the symbol duration    -   Random polarity from symbol to symbol    -   Identical sets of different polarities for pulses in the symbol        duration from symbol to symbol

Different modulation schemes

-   -   Random polarity of pulses within the symbol duration    -   Random polarity from symbol to symbol    -   Identical set of different polarities for pulses in symbol        duration

Random polarity for spectrum shaping

Random polarity of sub structure of a symbol—dual pulse waveform

One Pulse Per Symbol

As stated above, the randomization of the polarity of the whole symboleliminates the spectral lines of the power spectrum density. Thesesymbols have a specific waveform. A single pulse constitutes thiswaveform here. The power spectral density of the modulated signaldepends on the power spectral density of the pulse.

Pulse Position Modulation:

FIG. 5 shows an example pulse train 500 with a 2 PPM. The train isconstituted by pulses dithered in time as follows. The pulse codes alogical zero in its original position. The pulse is delayed to encode alogical one.

The discrete part of the power spectrum density of a dithered pulsetrain using a 2-PPM is given by Equation (4) as:

$\begin{matrix}{{G_{s}(f)} = {\frac{1}{T_{s}^{2}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}\;{\left( {{{\sum\limits_{i = 0}^{1}\;{P_{i} \cdot {S_{i}\left( \frac{n}{T_{s}} \right)}}}}^{2}{\delta\left( {f - \frac{n}{T_{s}}} \right)}} \right).}}}} & (4)\end{matrix}$

FIG. 6 shows the spectrum of this signal. FIG. 7 shows this signal afterinverting randomly the polarity of individual pulses. After invertingrandomly the polarity of the symbols, the discrete part of the powerspectrum density is given by Equation (5) as:

$\begin{matrix}{{G_{s}(f)} = {{\frac{1}{T_{s}^{2}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}\;\left( {{{\sum\limits_{i = 0}^{1}\;\left( {{\frac{P_{i}}{2} \cdot {S_{i}\left( \frac{n}{T_{s}} \right)}} - {\frac{P_{i}}{2} \cdot {S_{i}\left( \frac{n}{T_{s}} \right)}}} \right)}}^{2}{\delta\left( {f - \frac{n}{T_{s}}} \right)}} \right)}} = 0.}} & (5)\end{matrix}$

As shown in FIG. 8, inverting the polarity in such a way makes all thediscrete components, i.e., spectral lines, disappear to result in acontinuous spectrum.

FIG. 9 shows a system and method 900 for eliminating spectral lines in adithered UWB signal according to the invention. The system includes apulse generator 910, a modulator 920, and an inverter 930 coupledserially to an antenna 931. Generate pulses are dithered in time 920,i.e., by a time hopping sequence for multiuser access and by PPM formodulation, according to data symbols 940, and the polarity of resultantpulses are inverted according to a pseudo random number (PRN) 950.

Pulse Amplitude Modulation

Pulse amplitude modulation is accomplished by on/off keying (OOK)modulation, which is a special case of PAM. For every time period T_(p),zero is represented by a pulse, and one by no pulse as shown in FIG. 10.

The discrete part of the power spectrum density of a OOK modulatedsignal is given by Equation (6) as:

$\begin{matrix}{{G_{s}(f)} = {\frac{1}{T_{s}^{2}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}\;{\left( {{{P_{1} \cdot {S_{1}\left( \frac{n}{T_{s}} \right)}}}^{2}{\delta\left( {f - \frac{n}{T_{s}}} \right)}} \right).}}}} & (6)\end{matrix}$

FIG. 11 shows the spectrum of this signal.

FIG. 12 shows that after changing randomly the polarity of the symbols,the discrete part of the power spectrum density is eliminated as givenby Equation (7):

$\begin{matrix}{{{G_{s}(f)} = {{\frac{1}{T_{s}^{2}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}\;\left( {{{{\frac{P_{1}}{2} \cdot {S_{1}\left( \frac{n}{T_{s}} \right)}} - {\frac{P_{1}}{2} \cdot {S_{1}\left( \frac{n}{T_{s}} \right)}}}}^{2}{\delta\left( {f - \frac{n}{T_{s}}} \right)}} \right)}} = 0}},} & (7)\end{matrix}$

FIG. 13 shows the spectrum of this signal, and FIG. 14 shows the systemand method according to the invention to achieve this results.

Multiple Pulses Per Symbol

The waveform of each symbol can also be constituted by a combination ofindividual pulses.

Pulse Position Modulation

Random Polarity of Pulses within Symbol Duration

Here, the symbol is a combination of N pulses. By changing the polarityof the pulses randomly and independently within the symbol, and fromsymbol to symbol, the spectral lines are eliminated. FIG. 15 shows thesignal before 1501 and after 1502 inverting the polarity of randompulses.

Random Polarity of Pulses from Symbol to Symbol

Here, the symbol is a combination of N pulses. By changing randomlyindependently the polarity from symbol to symbol, the spectral lines areeliminated. FIG. 16 shows the signal before 1601 and after 1602 polarityinversion.

Identical Set of Different Polarities for Pulses in Symbol Duration

In this case, the symbol is a combination of N pulses. The polarity ofthe pulses within the symbol is randomly changed for each of the Msymbols of the constellation. A polarity pattern is thus affected foreach symbol of the constellation. FIG. 17 shows the signal before 1701and after 1702 random polarization inversion.

Pulse Amplitude Modulation

Here, the symbols are composed by a TH sequence whose amplitude varies.

Random Polarity of Pulses within Symbol Duration

The symbol is a combination of N pulses. By changing randomlyindependently the polarity of the pulses within the symbol and fromsymbol to symbol, as shown in FIG. 18, the spectral lines areeliminated.

Random Polarity of Pulses from Symbol to Symbol

The symbol is a combination of N pulses. By changing randomly thepolarity from symbol to symbol, as shown in FIG. 19, the spectral linesare eliminated.

Identical Set of Different Polarities for Pulses in Symbol Duration

The symbol is a combination of N pulses. The polarity of the pulseswithin the symbol is randomly changed for each of the M symbols of theconstellation, as shown in FIG. 20. A polarity pattern is thus affectedfor each symbol of the constellation.

Different Modulation Schemes

The random polarity can be applied to other modulation schemes. Thesymbols can be coded by different TH sequences for example. The m^(th)symbol is a combination of n_(m) pulses.

Random Polarity of Pulses within Symbol Duration

By changing randomly independently the polarity of the pulses within thesymbol and from symbol to symbol, as shown in FIG. 21, the spectrallines disappear.

Random Polarity of Pulses from Symbol to Symbol

By changing randomly independently the polarity from symbol to symbol,as shown in FIG. 22, the spectral lines disappear too.

Identical Set of Different Polarities for Pulses in Symbol Duration

The polarity of the pulses within the symbol can be randomly changed foreach of the M symbols of the constellation, as shown in FIG. 23. Apolarity pattern is thus affected for each symbol of the constellation.

Random Polarity for Spectrum Shaping

As described above, the spectral lines disappear when the polaritychanges from symbol to symbol. The continuous part of the spectrum canbe derived from Equation (1). The power spectrum of the signal beforepolarity changes is:

$\begin{matrix}{{G_{s}(f)} = {{\frac{1}{M^{2}T_{s}^{2}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}\;\left( {{{\sum\limits_{i = 0}^{M - 1}\;{S_{i}\left( \frac{n}{T_{s}} \right)}}}^{2}{\delta\left( {f - \frac{n}{T_{s}}} \right)}} \right)}} +}} \\{{\frac{1}{T_{s}}\left( {{\sum\limits_{i = 0}^{M - 1}\;{\frac{1}{M} \cdot {{S_{i}(f)}}^{2}}} - {{\sum\limits_{i = 0}^{M - 1}\;{\frac{1}{M} \cdot {S_{i}(f)}}}}^{2}} \right)},}\end{matrix}$

after polarity changes:

$\begin{matrix}{{G_{s}(f)} = {{\frac{1}{M^{2}T_{s}^{2}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}\;\left( {{{{\frac{1}{2}{\sum\limits_{i = 0}^{M - 1}\;{S_{i}\left( \frac{n}{T_{s}} \right)}}} + {\frac{1}{2}{\sum\limits_{j = 0}^{M - 1}\;{S_{j}\left( \frac{n}{T_{s}} \right)}}}}}^{2}{\delta\left( {f - \frac{n}{T_{s}}} \right)}} \right)}} +}} \\{\frac{1}{T_{s}}{\left( {{\sum\limits_{i = 0}^{M - 1}\;{\frac{1}{M} \cdot {{S_{i}(f)}}^{2}}} - {{{\frac{1}{M}{\sum\limits_{i = 0}^{M - 1}\;{\frac{1}{2}{S_{i}(f)}}}} + {\frac{1}{M}{\sum\limits_{j = 0}^{M - 1}\;{\frac{1}{2}{S_{j}(f)}}}}}}^{2}} \right).}}\end{matrix}$

The symbols s_(i+M) are the symbols s_(i) with an opposite polarity.Hence S_(i+M)=−S_(i) for i from 0 to M−1.

$\begin{matrix}\begin{matrix}{{G_{s}(f)} = {{{\frac{1}{M^{2}T_{s}^{2}} \cdot \frac{1}{2}}{\sum\limits_{n = {- \infty}}^{+ \infty}\;\left( {{{\sum\limits_{i = 0}^{M - 1}\;\left( {{S_{i}\left( \frac{n}{T_{s}} \right)} - {S_{i}\left( \frac{n}{T_{s}} \right)}} \right)}}^{2}{\delta\left( {f - \frac{n}{T_{s}}} \right)}} \right)}} +}} \\{\frac{1}{T_{s}}\left( {{\sum\limits_{i = 0}^{M - 1}\;{\frac{1}{M} \cdot {{S_{i}(f)}}^{2}}} - {{\frac{1}{2M}{\sum\limits_{i = 0}^{M - 1}\;\left( {{S_{i}(f)} - {S_{i}(f)}} \right)}}}^{2}} \right)} \\{{G_{s}(f)} = {\frac{1}{M \cdot T_{s}}{\sum\limits_{i = 0}^{M - 1}\;{{{S_{i}(f)}}^{2}.}}}}\end{matrix} & (8)\end{matrix}$

From Equation (8), it appears that the spectrum of the signal is definedby the summation of the spectrum of the symbols. For example if thesymbols have the same waveform, the spectral properties of the signalare identical to the spectral properties of this waveform.

That is the case for example for the PAM and PPM schemes. For the PPM,the same waveform is delayed in time, and for the PAM, the waveform isassociated with different amplitudes in order to create the differentsymbols.

Considering Equation (8), changing randomly the polarity from symbol tosymbol provides an efficient way to shape the spectrum. The task ofspectrum shaping of the signal is determined by the design of thewaveform.

Thus, the waveform of the symbol characterizes entirely the spectrum ofthe whole signal. If the spectrum of this waveform contains nulls, thenthe power spectral density function of the modulated signal gets thesame nulls.

For example, a TH sequence of four pulses constitutes the waveform ofthe symbol. The modulation is a 2PPM. Thus, the Fourier transform of theTH sequence defines the power spectral density of the total signal. Aswell as their position or amplitude, the polarity of these four pulsescan be used to shape the spectrum in order to create nulls in thespectrum.

In the example of FIG. 24, the modulation scheme is PAM. A TH sequenceconstitute the symbols. The polarity sequence for the pulses composingthe TH sequence modify the spectral characteristics of the signal.Furthermore, the polarity is random from symbol to symbol to eliminatespectral lines as shown in FIG. 25.

Random Polarity of Sub-Structures of Symbols

Here, the waveform of the symbol is a combination of several identicalsubwaveform dithered in time (PPM scheme). In addition, different pulseamplitude modulation (PAM) schemes can be applied. By changing randomlythe polarity of these substructure, the power spectral density of thesubstructure is identical to the power spectral density of the symbol,and thus, of the total signal.

This mode can be used for the design of a TH sequence for multi-userdetection with nulls at specific frequency in order to reduceinterference with narrow band systems.

In the example shown in FIG. 26, the subwaveform is a grouping of twopulses with an opposite polarity. FIG. 27 shows a TH sequence composedof four subwaveforms with two grouped pulses each. As shown in FIG. 28,the power spectrum density for this TH sequence does not have spectrallines and contains nulls periodically. One is at 5 GHz, i.e., notches2800, to avoid interference with the 802.11a standard.

Hence, the random polarity reversal eliminates the spectral lines,shapes the continuous part of the spectrum, and enables a flexibledesign of a multi-user receiver. This subwaveform can be used togenerate a TH sequence independently of the spectral characteristics ofthe symbols.

Although the invention has been described by way of examples ofpreferred embodiments, it is to be understood that various otheradaptations and modifications can be made within the spirit and scope ofthe invention. Therefore, it is the object of the appended claims tocover all such variations and modifications as come within the truespirit and scope of the invention.

1. A method for eliminating spectral lines in a time hopping ultra widebandwidth signal, comprising: generating a train of non-periodic pulses;modulating the non-periodic pulses in time according to uncorrelatedsymbols; and inverting, randomly, a polarity of the non-periodic pulsesbefore transmitting the non-periodic pulses as an ultra wide bandwidthsignal.
 2. The method of claim 1 wherein each uncorrelated symbolincludes one non-periodic pulse.
 3. The method of claim 2 wherein themodulation of the one non-periodic pulse per uncorrelated symbol ispulse position modulation.
 4. The method of claim 2 wherein themodulation of the one non-periodic pulse per uncorrelated symbol isamplitude modulation.
 5. The method of claim 2 wherein the modulation ofthe one non-periodic pulse per uncorrelated symbol is a combination ofamplitude modulation and pulse position modulation.
 6. The method ofclaim 4 wherein the pulse amplitude modulation is accomplished withon/off keying, wherein for every time period a zero is represented by anon-periodic pulse, and a one by no pulse.
 7. The method of claim 1wherein each uncorrelated symbol includes a combination of individualnon-periodic pulses.
 8. The method of claim 7 wherein the polarity of acombination of N non-periodic pulses of each uncorrelated symbol israndomly and independently inverted from uncorrelated symbol touncorrelated symbol.
 9. The method of claim 7 wherein the polarity ofindividual non-periodic pulses of each uncorrelated symbol are randomlyand independently inverted within each uncorrelated symbol and fromuncorrelated symbol to uncorrelated symbol.
 10. The method of claim 7wherein the polarity of individual non-periodic pulses of eachuncorrelated symbol are randomly inverted within each uncorrelatedsymbol and identically inverted from uncorrelated symbol to uncorrelatedsymbol.
 11. The method of claim 7 wherein the uncorrelated symbols aremodulated by pulse position modulation.
 12. The method of claim 7 wherethe uncorrelated symbols are modulated by amplitude modulation.
 13. Themethod of claim 7 wherein the uncorrelated symbols are modulated by acombination of pulse position modulation and amplitude modulation. 14.The method of claim 7 wherein the combination of non-periodic pulsesfollows a pattern of a time hopping sequence.
 15. The method of claim 14wherein different time hopping sequences are used to encode a sameuncorrelated symbol of a constellation.
 16. The method of claim 1further comprising: shaping a spectrum of the UWB signal to apredetermined shape by the random inverting of the polarity of thenon-periodic pulses.
 17. The method of claim 16 wherein the modulatingis pulse amplitude modulation.
 18. The method of claim 16 wherein themodulating is pulse position modulation.
 19. The method of claim 14wherein the modulating is a combination of pulse amplitude modulationand pulse position modulation.
 20. The method of claim 7 furthercomprising: shaping a spectrum of the UWB signal to a predeterminedshape by the random inverting of the polarity of the non-periodicpulses.
 21. The method of claim 20 wherein the modulating is pulseamplitude modulation.
 22. The method of claim 20 wherein the modulatingis pulse position modulation.
 23. The method of claim 20 wherein themodulating is a combination of pulse amplitude modulation and pulseposition modulation.
 24. The method of claim 9 further comprising:shaping a spectrum of the UWB signal to a predetermined shape by therandom inverting of the polarity of the non-periodic pulses.
 25. Themethod of claim 14 further comprising: shaping a spectrum of the UWBsignal to a predetermined shape by the random inverting of the polarityof the non-periodic pulses.
 26. The method of claim 1 furthercomprising: grouping sets of non-periodic pulses into subwaveforms; andmeans for inverting, randomly a polarity of the subwaveforms.
 27. Themethod of claim 26 further comprising: shaping a spectrum of the UWBsignal to a predetermined shape by the random inverting of the polarityof the subwaveforms.
 28. The method of claim 2 further comprising:grouping sets of uncorrelated symbols; means for inverting, randomly, apolarity of the uncorrelated symbols a first set of the sets ofuncorrelated symbols; and means for inverting a polarity of a next setof the sets of uncorrelated symbols according to the polarity of theuncorrelated symbols of the first set.
 29. A system for eliminatingspectral lines in a time hopping ultra wide bandwidth signal,comprising: means for generating a train of non-periodic pulses; meansfor modulating the non-periodic pulses in time according to uncorrelatedsymbols; and means for inverting, randomly, a polarity of thenon-periodic pulses before transmitting the non-periodic pulses as anultra wide bandwidth signal.